Recursive descent parsing for grammars with contexts

Grammars with contexts (B, Okhotin, 2012)A → α 1 & . . . & α k & ✄β 1 & . . . & ✄β m & γ 1 & . . . & γ nGiven a string x = u w v:each α i defines weach β i defines v (the right context of w)each γ i defines wv (the extended right context of w)Semantics by logical deduction of elementary propositions[X , 〈w〉v] : “a string w written in right context v has the property X ”{a n b n c} ∪ {a n b 2n d}S → Ac | BdA → aAb | ε L(A) = {a n b n }B → aBbb | ε L(B) = {a n b 2n }X → aX | bX | ε L(X ) = (a | b) ∗the language is not standard LL(k) for any kway out: use right contexts to peek the last symbol of the stringMikhail BarashRecursive descent for grammars with contexts